Finite Group Databasebeta

← C137×#11087 #46860473

Subgroups — C137×#11087 #46860473

Order 35072.

1478 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#99×C137C211yesmaximal, characteristic
2#2308×C137C211yesmaximal, characteristic
3C2×#386×C137C211yesmaximal, characteristic
4C2×#385×C137C211yesmaximal, characteristic, complemented
5C2×#342×C137C211yesmaximal, characteristic, complemented
6C2×#342×C137C211yesmaximal, characteristic, complemented
7C22⋊#95×C137C211yesmaximal, characteristic, complemented
8C23×D4×C137C2211yescharacteristic
9C24×C4×C137C2211yescharacteristic
10C22×C4⋊C4×C137—21no—
11C22×C22⋊C4×C137—21no—
12C22×C22⋊C4×C137C2211yescharacteristic
13C22×C22⋊C4×C137C2211yescharacteristic
14C22×C22⋊C4×C137C2211yescharacteristic
15C22×C22⋊C4×C137C2211yescharacteristic
16C22×C22⋊C4×C137C2211yescharacteristic
17C2×#99×C137—22no—
18C2×#99×C137—22no—
19C2×#99×C137C414yescomplemented
20#386×C137—22no—
21#386×C137—21no—
22#386×C137—22no—
23#386×C137—21no—
24#386×C137—22no—
25#385×C137—22no—
26#385×C137—22no—
27#381×C137—21no—
28#379×C137—21no—
29C2×#95×C137—21no—
30C2×#95×C137—21no—
31C2×#95×C137—22no—
32#342×C137—22no—
33#342×C137—22no—
34C25×C137D411yescharacteristic
35C25×C137C2311yescharacteristic
36C22×D4×C137—21no—
37C22×D4×C137—21no—
38C22×D4×C137—21no—
39C22×D4×C137—21no—
40C22×D4×C137—21no—
41C22×D4×C137—21no—
42C22×D4×C137—21no—
43C22×D4×C137—21no—
44C22×D4×C137—21no—
45C22×D4×C137—21no—
46C22×D4×C137—21no—
47C22×D4×C137—21no—
48C22×D4×C137C2×C412yes—
49C22×D4×C137Q812yes—
50C23×C4×C137—21no—
51C23×C4×C137—21no—
52C23×C4×C137—21no—
53C23×C4×C137—21no—
54C23×C4×C137—21no—
55C23×C4×C137—21no—
56C23×C4×C137—21no—
57C23×C4×C137—21no—
58C23×C4×C137—21no—
59C23×C4×C137—44no—
60C23×C4×C137D411yescharacteristic
61C23×C4×C137D411yescharacteristic
62C23×C4×C137D412yes—
63C23×C4×C137D412yes—
64C23×C4×C137D411yescharacteristic
65C2×C4⋊C4×C137—24no—
66C2×C4⋊C4×C137—44no—
67C2×C22⋊C4×C137—21no—
68C2×C22⋊C4×C137—21no—
69C2×C22⋊C4×C137—21no—
70C2×C22⋊C4×C137—21no—
71C2×C22⋊C4×C137—21no—
72C2×C22⋊C4×C137—21no—
73C2×C22⋊C4×C137—21no—
74C2×C22⋊C4×C137—21no—
75C2×C22⋊C4×C137—21no—
76C2×C22⋊C4×C137—21no—
77C2×C22⋊C4×C137—21no—
78C2×C22⋊C4×C137—24no—
79C2×C22⋊C4×C137—21no—
80C2×C22⋊C4×C137—21no—
81C2×C22⋊C4×C137—21no—
82C2×C22⋊C4×C137—21no—
83C2×C22⋊C4×C137—21no—
84C2×C22⋊C4×C137—21no—
85C2×C22⋊C4×C137—21no—
86C2×C22⋊C4×C137—21no—
87C2×C22⋊C4×C137—21no—
88C2×C22⋊C4×C137—21no—
89C2×C22⋊C4×C137—21no—
90C2×C22⋊C4×C137—21no—
91C2×C22⋊C4×C137—21no—
92C2×C22⋊C4×C137—21no—
93C2×C22⋊C4×C137—22no—
94C2×C22⋊C4×C137—22no—
95C2×C22⋊C4×C137—44no—
96C2×C22⋊C4×C137C2×C412yes—
97C2×C22⋊C4×C137C2×C412yes—
98C2×C22⋊C4×C137D412yes—
99C2×C22⋊C4×C137D412yes—
100C2×C22⋊C4×C137D412yes—
101#99×C137—28no—
102#95×C137—24no—
103#95×C137—24no—
104#95×C137—22no—
105#95×C137—22no—
106#95×C137—44no—
107C24×C137—21no—
108C24×C137—21no—
109C24×C137—21no—
110C24×C137—21no—
111C24×C137—21no—
112C24×C137—21no—
113C24×C137—42no—
114C24×C137—42no—
115C24×C137—42no—
116C24×C137—42no—
117C24×C137C4⋊C412yescomplemented
118C24×C137C22×C411yescharacteristic
119C24×C137C2×D411yescharacteristic
120C24×C137C2×D411yescharacteristic
121C24×C137C2×D411yescharacteristic
122C24×C137C2×D411yescharacteristic
123C24×C137C2×D411yescharacteristic
124C24×C137C2×D411yescharacteristic
125C24×C137C2×D411yescharacteristic
126C24×C137C2×Q811yescharacteristic
127C24×C137#4111yescharacteristic
128C24×C137#4111yescharacteristic
129C24×C137#4111yescharacteristic
130C24×C137#4111yescharacteristic
131C24×C137#4111yescharacteristic
132C24×C137#4111yescharacteristic
133C2×D4×C137—22no—
134C2×D4×C137—22no—
135C2×D4×C137—22no—
136C2×D4×C137—22no—
137C2×D4×C137—22no—
138C2×D4×C137—22no—
139C2×D4×C137—22no—
140C2×D4×C137—22no—
141C2×D4×C137—22no—
142C2×D4×C137—22no—
143C2×D4×C137—22no—
144C2×D4×C137—22no—
145C2×D4×C137—41no—
146C2×D4×C137—41no—
147C2×D4×C137—41no—
148C2×D4×C137—41no—
149C2×D4×C137—41no—
150C2×D4×C137—41no—
151C2×D4×C137—41no—
152C2×D4×C137—41no—
153C2×D4×C137—41no—
154C2×D4×C137—41no—
155C2×D4×C137—41no—
156C2×D4×C137—41no—
157C2×D4×C137—41no—
158C2×D4×C137—41no—
159C2×D4×C137—41no—
160C2×D4×C137—41no—
161C22×C4×C137—24no—
162C22×C4×C137—24no—
163C22×C4×C137—24no—
164C22×C4×C137—22no—
165C22×C4×C137—21no—
166C22×C4×C137—22no—
167C22×C4×C137—22no—
168C22×C4×C137—22no—
169C22×C4×C137—21no—
170C22×C4×C137—22no—
171C22×C4×C137—22no—
172C22×C4×C137—21no—
173C22×C4×C137—21no—
174C22×C4×C137—21no—
175C22×C4×C137—21no—
176C22×C4×C137—22no—
177C22×C4×C137—21no—
178C22×C4×C137—22no—
179C22×C4×C137—21no—
180C22×C4×C137—21no—
181C22×C4×C137—21no—
182C22×C4×C137—22no—
183C22×C4×C137—22no—
184C22×C4×C137—21no—
185C22×C4×C137—21no—
186C22×C4×C137—22no—
187C22×C4×C137—44no—
188C22×C4×C137—44no—
189C22×C4×C137—44no—
190C22×C4×C137—44no—
191C22×C4×C137—42no—
192C22×C4×C137—42no—
193C22×C4×C137—42no—
194C22×C4×C137—42no—
195C22×C4×C137—42no—
196C22×C4×C137—41no—
197C22×C4×C137—41no—
198C22×C4×C137—41no—
199C22×C4×C137—41no—
200C22×C4×C137—42no—
201C22×C4×C137—42no—
202C22×C4×C137—42no—
203C22×C4×C137—42no—
204C22×C4×C137—42no—
205C22×C4×C137—42no—
206C22×C4×C137—42no—
207C22×C4×C137—42no—
208C22×C4×C137—41no—
209C22×C4×C137—41no—
210C22×C4×C137—41no—
211C22×C4×C137—41no—
212C22×C4×C137C4⋊C412yescomplemented
213C4⋊C4×C137—48no—
214C22⋊C4×C137—22no—
215C22⋊C4×C137—22no—
216C22⋊C4×C137—22no—
217C22⋊C4×C137—22no—
218C22⋊C4×C137—22no—
219C22⋊C4×C137—22no—
220C22⋊C4×C137—22no—
221C22⋊C4×C137—48no—
222C22⋊C4×C137—41no—
223C22⋊C4×C137—41no—
224C22⋊C4×C137—41no—
225C22⋊C4×C137—41no—
226C22⋊C4×C137—41no—
227C22⋊C4×C137—41no—
228C22⋊C4×C137—41no—
229C22⋊C4×C137—41no—
230C22⋊C4×C137—41no—
231C22⋊C4×C137—41no—
232C22⋊C4×C137—41no—
233C22⋊C4×C137—41no—
234C22⋊C4×C137—82no—
235C22⋊C4×C137—82no—
236C22⋊C4×C137C22⋊C414yescomplemented
237C23×C137—22no—
238C23×C137—22no—
239C23×C137—22no—
240C23×C137—22no—
241C23×C137—22no—
242C23×C137—22no—
243C23×C137—22no—
244C23×C137—22no—
245C23×C137—22no—
246C23×C137—41no—
247C23×C137—41no—
248C23×C137—41no—
249C23×C137—41no—
250C23×C137—42no—
251C23×C137—41no—
252C23×C137—41no—
253C23×C137—41no—
254C23×C137—42no—
255C23×C137—42no—
256C23×C137—42no—
257C23×C137—42no—
258C23×C137—41no—
259C23×C137—42no—
260C23×C137—42no—
261C23×C137—42no—
262C23×C137—44no—
263C23×C137—42no—
264C23×C137—42no—
265C23×C137—44no—
266C23×C137—41no—
267C23×C137—41no—
268C23×C137—41no—
269C23×C137—41no—
270C23×C137—42no—
271C23×C137—42no—
272C23×C137—82no—
273C23×C137—81no—
274C23×C137—81no—
275C23×C137—82no—
276C23×C137C2×C22⋊C411yescharacteristic
277C23×C137C2×C4⋊C411yescharacteristic
278C23×C137#11711yescharacteristic
279C23×C137C4×D411yescharacteristic
280C23×C137C4×D411yescharacteristic
281C23×C137C4×D411yescharacteristic
282C23×C137C4×D411yescharacteristic
283C23×C137#12011yescharacteristic
284C23×C137#12011yescharacteristic
285C23×C137#12011yescharacteristic
286C23×C137#12111yescharacteristic
287C23×C137#12111yescharacteristic
288C23×C137#12111yescharacteristic
289C23×C137#12111yescharacteristic
290C23×C137#12111yescharacteristic
291C23×C137#12111yescharacteristic
292C23×C137#12111yescharacteristic
293C23×C137#12111yescharacteristic
294C23×C137C22⋊Q811yescharacteristic
295C23×C137C22⋊Q811yescharacteristic
296C23×C137C22⋊Q811yescharacteristic
297C23×C137C22⋊Q811yescharacteristic
298C23×C137C22⋊Q811yescharacteristic
299C23×C137C22⋊Q811yescharacteristic
300C23×C137#12311yescharacteristic
301C23×C137#12311yescharacteristic
302C23×C137#12311yescharacteristic
303C23×C137#12311yescharacteristic
304C23×C137#12311yescharacteristic
305C23×C137#12411yescharacteristic
306C23×C137#12411yescharacteristic
307C23×C137#12411yescharacteristic
308C23×C137#12611yescharacteristic
309C23×C137#12611yescharacteristic
310C23×C137#12711yescharacteristic
311D4×C137—42no—
312D4×C137—42no—
313D4×C137—42no—
314D4×C137—42no—
315D4×C137—42no—
316D4×C137—42no—
317D4×C137—42no—
318D4×C137—42no—
319C2×C4×C137—24no—
320C2×C4×C137—24no—
321C2×C4×C137—24no—
322C2×C4×C137—22no—
323C2×C4×C137—22no—
324C2×C4×C137—22no—
325C2×C4×C137—24no—
326C2×C4×C137—42no—
327C2×C4×C137—44no—
328C2×C4×C137—42no—
329C2×C4×C137—44no—
330C2×C4×C137—42no—
331C2×C4×C137—42no—
332C2×C4×C137—42no—
333C2×C4×C137—44no—
334C2×C4×C137—44no—
335C2×C4×C137—44no—
336C2×C4×C137—42no—
337C2×C4×C137—41no—
338C2×C4×C137—41no—
339C2×C4×C137—41no—
340C2×C4×C137—41no—
341C2×C4×C137—44no—
342C2×C4×C137—42no—
343C2×C4×C137—42no—
344C2×C4×C137—44no—
345C2×C4×C137—42no—
346C2×C4×C137—42no—
347C2×C4×C137—44no—
348C2×C4×C137—42no—
349C2×C4×C137—41no—
350C2×C4×C137—41no—
351C2×C4×C137—42no—
352C2×C4×C137—42no—
353C2×C4×C137—42no—
354C2×C4×C137—42no—
355C2×C4×C137—42no—
356C2×C4×C137—42no—
357C2×C4×C137—82no—
358C2×C4×C137—81no—
359C2×C4×C137—81no—
360C2×C4×C137—82no—
361C2×C4×C137—82no—
362C2×C4×C137—81no—
363C2×C4×C137—81no—
364C2×C4×C137—82no—
365C22×C137—22no—
366C22×C137—22no—
367C22×C137—22no—
368C22×C137—22no—
369C22×C137—22no—
370C22×C137—22no—
371C22×C137—21no—
372C22×C137—21no—
373C22×C137—21no—
374C22×C137—21no—
375C22×C137—21no—
376C22×C137—21no—
377C22×C137—21no—
378C22×C137—21no—
379C22×C137—21no—
380C22×C137—21no—
381C22×C137—21no—
382C22×C137—21no—
383C22×C137—22no—
384C22×C137—22no—
385C22×C137—22no—
386C22×C137—22no—
387C22×C137—22no—
388C22×C137—22no—
389C22×C137—41no—
390C22×C137—41no—
391C22×C137—41no—
392C22×C137—41no—
393C22×C137—41no—
394C22×C137—41no—
395C22×C137—41no—
396C22×C137—41no—
397C22×C137—41no—
398C22×C137—41no—
399C22×C137—41no—
400C22×C137—41no—
401C22×C137—41no—
402C22×C137—41no—
403C22×C137—41no—
404C22×C137—41no—
405C22×C137—44no—
406C22×C137—44no—
407C22×C137—42no—
408C22×C137—82no—
409C22×C137—82no—
410C22×C137—82no—
411C22×C137—81no—
412C22×C137—81no—
413C22×C137—82no—
414C22×C137#38011yescharacteristic
415C22×C137#38511yescharacteristic
416C22×C137#38511yescharacteristic
417C22×C137#38611yescharacteristic
418C22×C137#38811yescharacteristic
419C22×C137#38811yescharacteristic
420C22×C137#39011yescharacteristic
421C22×C137#39211yescharacteristic
422C22×C137#39311yescharacteristic
423C22×C137#39411yescharacteristic
424C22×C137#39411yescharacteristic
425C22×C137#39611yescharacteristic
426C22×C137#39611yescharacteristic
427C22×C137#39711yescharacteristic
428C22×C137#39911yescharacteristic
429C22×C137B(4,𝔽2)12yes—
430C22×C137#45812yes—
431C4×C137—44no—
432C4×C137—42no—
433C4×C137—44no—
434C4×C137—82no—
435C4×C137—82no—
436C4×C137—81no—
437C4×C137—81no—
438C4×C137—82no—
439C2×C137—21no—
440C2×C137—21no—
441C2×C137—21no—
442C2×C137—21no—
443C2×C137—21no—
444C2×C137—21no—
445C2×C137—21no—
446C2×C137—21no—
447C2×C137—21no—
448C2×C137—21no—
449C2×C137—21no—
450C2×C137—21no—
451C2×C137—82no—
452C2×C137#143911yescharacteristic
453C2×C137#186712yes—
454C2×C137#202111yescharacteristic
455C2×C137#202211yescharacteristic
456C2×C137#204412yes—
457#11087C13711yesmaximal, characteristic, direct product factor, Sylow
458C137#1108711yescharacteristic, direct product factor, Sylow
459C22×#99C2×C13711yescharacteristic
460#2308C2×C13711yescharacteristic
461C2×#386C2×C13711yescharacteristic
462C2×#385C2×C13711yescharacteristic, complemented
463C2×#342C2×C13711yescharacteristic, complemented
464C2×#342C2×C13711yescharacteristic, complemented
465C22⋊#95C2×C13711yescharacteristic, complemented
466C23×D4C22×C13711yescharacteristic
467C24×C4C22×C13711yescharacteristic
468C22×C4⋊C4—21no—
469C22×C22⋊C4—21no—
470C22×C22⋊C4C22×C13711yescharacteristic
471C22×C22⋊C4C22×C13711yescharacteristic
472C22×C22⋊C4C22×C13711yescharacteristic
473C22×C22⋊C4C22×C13711yescharacteristic
474C22×C22⋊C4C22×C13711yescharacteristic
475C2×#99—22no—
476C2×#99—22no—
477C2×#99C4×C13714yescomplemented
478#386—21no—
479#386—21no—
480#386—22no—
481#386—22no—
482#386—22no—
483#385—22no—
484#385—22no—
485#381—21no—
486#379—21no—
487C2×#95—21no—
488C2×#95—21no—
489C2×#95—22no—
490#342—22no—
491#342—22no—
492C25D4×C13711yescharacteristic
493C25C23×C13711yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4C2×C4×C13712yes—
507C22×D4Q8×C13712yes—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—44no—
518C23×C4D4×C13711yescharacteristic
519C23×C4D4×C13711yescharacteristic
520C23×C4D4×C13711yescharacteristic
521C23×C4D4×C13712yes—
522C23×C4D4×C13712yes—
523C2×C4⋊C4—24no—
524C2×C4⋊C4—44no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—44no—
554C2×C22⋊C4C2×C4×C13712yes—
555C2×C22⋊C4C2×C4×C13712yes—
556C2×C22⋊C4D4×C13712yes—
557C2×C22⋊C4D4×C13712yes—
558C2×C22⋊C4D4×C13712yes—
559#99—28no—
560#95—24no—
561#95—24no—
562#95—22no—
563#95—22no—
564#95—44no—
565C24—21no—
566C24—21no—
567C24—21no—
568C24—21no—
569C24—21no—
570C24—21no—
571C24—42no—
572C24—42no—
573C24—42no—
574C24—42no—
575C24C4⋊C4×C13712yescomplemented
576C24C22×C4×C13711yescharacteristic
577C24C2×D4×C13711yescharacteristic
578C24C2×D4×C13711yescharacteristic
579C24C2×D4×C13711yescharacteristic
580C24C2×D4×C13711yescharacteristic
581C24C2×D4×C13711yescharacteristic
582C24C2×D4×C13711yescharacteristic
583C24C2×D4×C13711yescharacteristic
584C24C2×Q8×C13711yescharacteristic
585C24#41×C13711yescharacteristic
586C24#41×C13711yescharacteristic
587C24#41×C13711yescharacteristic
588C24#41×C13711yescharacteristic
589C24#41×C13711yescharacteristic
590C24#41×C13711yescharacteristic
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—41no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—41no—
609C2×D4—41no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4—41no—
616C2×D4—41no—
617C2×D4—41no—
618C2×D4—41no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—24no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—21no—
641C22×C4—22no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—22no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—41no—
670C22×C4C4⋊C4×C13712yescomplemented
671C4⋊C4—48no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—48no—
680C22⋊C4—41no—
681C22⋊C4—41no—
682C22⋊C4—41no—
683C22⋊C4—41no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—41no—
689C22⋊C4—41no—
690C22⋊C4—41no—
691C22⋊C4—41no—
692C22⋊C4—82no—
693C22⋊C4—82no—
694C22⋊C4C22⋊C4×C13714yescomplemented
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—42no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—42no—
713C23—42no—
714C23—41no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—44no—
721C23—42no—
722C23—42no—
723C23—44no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—82no—
731C23—81no—
732C23—81no—
733C23—82no—
734C23C2×C22⋊C4×C13711yescharacteristic
735C23C2×C4⋊C4×C13711yescharacteristic
736C23#117×C13711yescharacteristic
737C23C4×D4×C13711yescharacteristic
738C23C4×D4×C13711yescharacteristic
739C23C4×D4×C13711yescharacteristic
740C23C4×D4×C13711yescharacteristic
741C23#120×C13711yescharacteristic
742C23#120×C13711yescharacteristic
743C23#120×C13711yescharacteristic
744C23#121×C13711yescharacteristic
745C23#121×C13711yescharacteristic
746C23#121×C13711yescharacteristic
747C23#121×C13711yescharacteristic
748C23#121×C13711yescharacteristic
749C23#121×C13711yescharacteristic
750C23#121×C13711yescharacteristic
751C23#121×C13711yescharacteristic
752C23C22⋊Q8×C13711yescharacteristic
753C23C22⋊Q8×C13711yescharacteristic
754C23C22⋊Q8×C13711yescharacteristic
755C23C22⋊Q8×C13711yescharacteristic
756C23C22⋊Q8×C13711yescharacteristic
757C23C22⋊Q8×C13711yescharacteristic
758C23#123×C13711yescharacteristic
759C23#123×C13711yescharacteristic
760C23#123×C13711yescharacteristic
761C23#123×C13711yescharacteristic
762C23#123×C13711yescharacteristic
763C23#124×C13711yescharacteristic
764C23#124×C13711yescharacteristic
765C23#124×C13711yescharacteristic
766C23#126×C13711yescharacteristic
767C23#126×C13711yescharacteristic
768C23#127×C13711yescharacteristic
769D4—42no—
770D4—42no—
771D4—42no—
772D4—42no—
773D4—42no—
774D4—42no—
775D4—42no—
776D4—42no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—81no—
816C2×C4—81no—
817C2×C4—82no—
818C2×C4—82no—
819C2×C4—82no—
820C2×C4—81no—
821C2×C4—81no—
822C2×C4—82no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—44no—
864C22—44no—
865C22—42no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22—81no—
870C22—81no—
871C22—82no—
872C22#380×C13711yescharacteristic
873C22#385×C13711yescharacteristic
874C22#385×C13711yescharacteristic
875C22#386×C13711yescharacteristic
876C22#388×C13711yescharacteristic
877C22#388×C13711yescharacteristic
878C22#390×C13711yescharacteristic
879C22#392×C13711yescharacteristic
880C22#393×C13711yescharacteristic
881C22#394×C13711yescharacteristic
882C22#394×C13711yescharacteristic
883C22#396×C13711yescharacteristic
884C22#396×C13711yescharacteristic
885C22#397×C13711yescharacteristic
886C22#399×C13711yescharacteristic
887C22B(4,𝔽2)×C13712yes—
888C22#458×C13712yes—
889C4—44no—
890C4—44no—
891C4—42no—
892C4—82no—
893C4—82no—
894C4—81no—
895C4—81no—
896C4—82no—
897C2—21no—
898C2—21no—
899C2—21no—
900C2—21no—
901C2—21no—
902C2—21no—
903C2—21no—
904C2—21no—
905C2—21no—
906C2—21no—
907C2—21no—
908C2—21no—
909C2—82no—
910C2#1439×C13711yescharacteristic
911C2#1867×C13712yes—
912C2#2021×C13711yescharacteristic
913C2#2022×C13711yescharacteristic
914C2#2044×C13712yes—
subgroupG/H
center, socleC23×C137#120
commutatorC24C22×C4×C137
Frattini, cosocleC25C23×C137
prime radicalC23×D4×C137C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C25×C137 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C2×#385×C137C2semidirect
5. C2×#342×C137C2semidirect
6. C2×#342×C137C2semidirect
7. C22⋊#95×C137C2semidirect
19. C2×#99×C137C4semidirect
117. C24×C137C4⋊C4semidirect
212. C22×C4×C137C4⋊C4semidirect
236. C22⋊C4×C137C22⋊C4semidirect
457. #11087C137direct (N × H)
458. C137#11087direct (N × H)
462. C2×#385C2×C137semidirect
463. C2×#342C2×C137semidirect
464. C2×#342C2×C137semidirect
465. C22⋊#95C2×C137semidirect
477. C2×#99C4×C137semidirect
575. C24C4⋊C4×C137semidirect
670. C22×C4C4⋊C4×C137semidirect
694. C22⋊C4C22⋊C4×C137semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#99×C1372
#2308×C1372
C2×#386×C1372
C2×#385×C1372
C2×#342×C1372
C22⋊#95×C1372
#11087137